Elliptic curve isogeny class 1225.3-j over number field \(\Q(\sqrt{21}) \)

• Base field: \(\Q(\sqrt{21}) \)
• Label: 2.2.21.1-1225.3-j
• Conductor: 1225.3
• Rank: \( 1 \)

Base field \(\Q(\sqrt{21}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 5 \); class number \(1\).

Elliptic curves in class 1225.3-j over \(\Q(\sqrt{21}) \)

Isogeny class 1225.3-j contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
1225.3-j1	\( \bigl[0\) , \( a - 1\) , \( a + 1\) , \( 548 a - 1538\) , \( 10243 a - 28589\bigr] \)
1225.3-j2	\( \bigl[0\) , \( 1\) , \( a + 1\) , \( 1435 a + 2182\) , \( 135297 a + 239275\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph